Some qualitative properties of mild solutions of a second-order integro-differential inclusion

Open Access

Original research article

Author(s):

Aurelian Cernea

Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania;
Academy of Romanian Scientists, Splaiul Independenței 54, 050094 Bucharest, Romania

Advances in the Theory of Nonlinear Analysis and its Applications 3(3), 141-149.

Received: August 28, 2019

Accepted: September 15, 2019

Published: September 18, 2019

Abstract

We establish the Lipschitz dependence on the initial data of the solution set for a Cauchy problem associated with a second-order integro-differential inclusion. The analysis is based on the contraction principle applied in the space of selections of the multifunction rather than in the space of solutions. Additionally, a Filippov-type existence theorem for this problem is provided.

Keywords: Differential inclusion, contraction principle, fixed point.

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APA Style

Cernea, A. (2019). Some qualitative properties of mild solutions of a second-order integro-differential inclusion. Advances in the Theory of Nonlinear Analysis and its Application, 3(3), 141-149.